1) Let X and Y the two events such P(X)=13 , P(X∣Y)=12, P(Y∣X)=25 Then A) P(Y)=415 B) P(X′∣Y)=12 C) P(X∪Y)=25 D) P(X∩Y)=15 Answer: Option A,BExplanation:P(X)=13 P(XY)=P(X∩Y)P(Y)=12 P(YX)=P(X∩Y)P(X)=25 P(X∩Y)=215 P(Y)=415 P(X′Y)=P(Y)−P(X∩Y)P(Y) =415−215415=12 P(X∪Y)=13+415−215 = 715=715